Reduce frequency of default browser dialog

[emerick]

Resolves brave/brave-browser#14502

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally: npm run test -- brave_browser_tests, npm run test -- brave_unit_tests, npm run lint, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on
• All relevant documentation has been updated, for instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

1. Launch browser with any profile (clean or existing both are fine)
2. Repeat launch and check default browser dialog is launched 3rd and 20th launching
3. Set as default
4. Launch browser and check dialog is not launched anymore
5. Set another browser as a default browser
6. Repeat launch and check default browser dialog is launched 3rd and 20th launching

Note If active tab is welcome page, dialog is not visible even if it's 3rd or 20th launching.

[mkarolin]

LGTM

[rebron]

Looks good.

[simonhong]

++

[simonhong]

@emerick curious why you run this only on iOS CI?

[emerick]

@simonhong The first CI run passed on all but iOS. Thanks for mentioning, forgot to mention it here.

[simonhong]

@emerick Ah. ok!

[emerick]

iOS completed successfully, merging now.